Question

# A daily commuter crosses two traffic signals on his way to work. The probability that he...

A daily commuter crosses two traffic signals on his way to work. The probability that he will be stopped at the first signal is 0.37, at the second signal is 0.5, and at both signals is 0.29.

What is the probability that a the commuter will be stopped at at least one of the signals?

What is the probability that he will be stopped at the first, but not the second signal?

What is the probability that he will be stopped at exactly one signal?

What is the probability that a the commuter will be stopped at at least one of the signals?

P(First OR second) =P(First)+P(Second)-P(First AND second) = 0.37+0.5-0.29 = 0.58

What is the probability that he will be stopped at the first, but not the second signal?

P(first not second) = P(only first) = 0.37-0.29 = 0.08

What is the probability that he will be stopped at exactly one signal?

P(exactly one) = P(First)+P(Second)-2*P(First AND second) = 0.37+0.5-2*0.29 = 0.29

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